arXiv subjects

Dmitriy G. Pak

Publications and source records attributed to Dmitriy G. Pak.

3 recordsLinked to original sources

arXiv2025

Non-perturbative on-shell multiplet structure of SU(N) Yang-Mills fields

Color multiplets of the gauge fields and fermions on mass shell in SU(N) Yang-Mills theory are classified according to representations of the Weyl group W(SU(N)). The multiplet structure of quark and gluon multiplets has been studied in the framework of a non-perturbative approach by considering complete exact equations of motion of the SU(N) Yang-Mills theory with matter fields. An important case of singlet non-Abelian gluon solutions corresponding to one-dimensional singlet representations of the Weyl group is revised on a rigorous mathematical basis. We demonstrate that Weyl group as a finite color subgroup of SU(N) reveals an inherent color symmetry of quarks and gluons on mass shell which determines a universal color miltiplet structure of quark-gluon solutions in a pure SU(N) Yang-Mills theory and in Abelian projected Yang-Mills theories with quarks. The obtained results allow to introduce strict concepts of fundamental particles, quarks and gluons, which differ drastically from the particle definitions in the conventional perturbative Yang-Mills theory. Possible applications of our results in non-perturbative quantum chromodynamics and hadron physics are discussed.

hep-th↗

arXiv2025

Weyl multiplet structure of QCD

Weyl group symmetric structure of SU(3) quantum chromodynamics (QCD) with one flavor quark is considered. It has been demonstrated that Weyl group as a finite color subgroup of SU(3) provides an intrinsic color symmetry of quark and gluon fields on mass shell. We show that standard QCD equations of motion lead to systems of equations for quarks and gluons forming non-trivial irreducible multiplets in one- and two-dimensional representations of the Weyl group. Some implications of Weyl multiplet structure in QCD and hadron physics are considered.

hep-th↗

arXiv2020

Inherent color symmetry of quantum Yang-Mills theory

We present the basic non-perturbative structure of the space of classical dynamical solutions and corresponding one particle quantum states in SU(3) Yang-Mills theory. It has been demonstrated that the Weyl group of su(3) algebra plays an important role in constructing non-perturbative solutions and leads to profound changes in the structure of the classical and quantum Yang-Mills theory. We show that the Weyl group as a non-trivial color subgroup of SU(3) admits singlet irreducible representations on a space of classical dynamical solutions which lead to strict concepts of one particle quantum states for gluons and quarks. The Yang-Mills theory is a non-linear theory and, in general, it is not possible to construct a Hilbert space of classical solutions and quantum states as a linear vector space, so, usually, a perturbative approach is applied. We propose a non-perturbative approach based on Weyl symmetric solutions to full non-linear equations of motion and construct a full space of dynamical solutions representing an infinite but countable solution space classified by a finite set of integer numbers. It has been proved that the Weyl singlet structure of classical solutions provides the existence of a stable non-degenerate vacuum which serves as a main precondition of the color confinement phenomenon. Some physical implications in quantum chromodynamics are considered.

hep-th↗